At QT Sugar factory the amounts which go into bag of sugar are supposed to be normally distributed with mean 36 kg and standard deviation 0.1 kg. Once every 30 minutes a bag is selected from the...

At QT Sugar factory the amounts which go into bag of sugar are supposed to be normally distributed with mean 36 kg and standard deviation 0.1 kg. Once every 30 minutes a bag is selected from the production line, and its contents are noted precisely. If the amount of the bag goes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control. a) If the process is in control, meaning u = 36 kg and o= 0.1 kg, find the probability that the bag will be declared out of control. b) In the situation of (a), find the probability that the number of bag found out of control in an eight-hour day (16 inspections) will be zero. c) In the situation of (a), find the probability that the number of bag found out control in an eight- hour day (16 inspections) will be exactly one. d) If the process shifts so that u =37 kg and o=0.4 kg find the probability that a bag will be declared out of control.

Extracted text: At QT Sugar factory the amounts which go into bag of sugar are supposed to be normally distributed with mean 36 kg and standard deviation 0.1 kg. Once every 30 minutes a bag is selected from the production line, and its contents are noted precisely. If the amount of the bag goes below 35.8 kg or above 36.2 kg, then the bag will be declared out of control. a) If the process is in control, meaning u = 36 kg and o= 0.1 kg, find the probability that the bag will be declared out of control. b) In the situation of (a), find the probability that the number of bag found out of control in an eight-hour day (16 inspections) will be zero. In the situation of (a), find the probability that the number of bag found out control in an eight- hour day (16 inspections) will be exactly one. d) If the process shifts so that u =37 kg and o=0.4 kg find the probability that a bag will be declared out of control.